Problem: Solve for $x$ : $x^2 - 11x + 10 = 0$
Answer: The coefficient on the $x$ term is $-11$ and the constant term is $10$ , so we need to find two numbers that add up to $-11$ and multiply to $10$ The two numbers $-10$ and $-1$ satisfy both conditions: $ {-10} + {-1} = {-11} $ $ {-10} \times {-1} = {10} $ $(x {-10}) (x {-1}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -10) (x -1) = 0$ $x - 10 = 0$ or $x - 1 = 0$ Thus, $x = 10$ and $x = 1$ are the solutions.